ASSUMING [tex]x^2-11xy-60y^2[/tex] is the expression to be factored.
where
a=1
b=-11
c=-60
We look for m, n such that m+n=b=-11, mn=c=-60.
It is possible to find m, n mentally, or compile a table as follows:
-1*60=-60, -1+60=59 > -11
-2*30=-60, -2+30=28 > -11
-3*20=-60, -3+20=17 > -11
-4*15=-60, -4+15=11 > -11
But 4*(-15)=-60, and 4-15=-11, exactly what we want!
So
[tex]x^2-11xy-60y^2=(x+4)(x-15)[/tex]
